CONTENTS. 



XV 



CHAPTER IX. 



SURFACE WAVES. 



ART. 1 AOE 



216. Statement of problem. Surface- conditions . . . 370 



217. Application to canal of unlimited length. Standing waves. 



Motion of particles . . . . -.-.- . 372 



218. Progressive waves. Wave- velocity. Elliptic orbits of 



particles. Numerical tables. . . . . . 374 



219. Energy of wave-system . . . . . . . 378 



220. General solution in terms of initial circumstances . . 379 



221. Group-velocity. Wave-resistance ^ , . . . 381 



222. Artifice of steady motion. Stationary undulations . . 384 

 223-225. Oscillations of the common surface of two liquids, or of 



two currents. Instability .. 385 



226-229. Surface disturbance of a stream. Effect of a simple- 

 harmonic application of pressure. Effect of a line of 

 pressure. Effect of a pressure-point. Ship-waves. 



Case of finite depth 393 



230. Effect of inequalities in the bed of a stream . . . 407 



231-235. Waves of finite amplitude. Stokes wave of permanent 

 type. Momentum. Gerstner s rotational waves. 

 Solitary wave. Connection with general dynamical 

 theory . . . . . . . . . 409 



236. Standing waves in limited masses of water. Case of 



uniform depth . . . . . . . 424 



237, 238. Standing waves with variable depth. Oscillations across 



a canal of triangular section. Approximate determina 

 tion of longest period for the case of semicircular 

 section 426 



239, 240. General theory of waves in uniform canal. Special pro 

 blems ; triangular section 429 



241-243. Gravitational oscillations of a liquid globe. Method of 



energy. Ocean of uniform depth .... 436 



244. Capillarity; surface-condition . . . . 442 



245. Capillary waves on the common surface of two liquids . 443 



246. 247. Waves due to joint action of gravity and cohesion. Mini 



mum wave-velocity. Group-velocity. Waves on the 

 common boundary of two currents ; stability . . 445 



248-250. Surface disturbance of a stream. Simple-harmonic dis 

 tribution of pressure. Effect of a local pressure. 

 Waves and ripples. Fish-line problem . . . 450 



251, 252. Vibrations of a cylindrical jet. Instability of a jet for 



varicose disturbance 457 



253. Vibrations of a spherical globule, and of a bubble . . 461 



